As of Saturday, Wright had been cleared to run and play catch. Boston interim manager Torey Lovullo added that Wright's rehab could expand to include a light throwing program soon.
"Still a little bit away," Wright said. "My balance is still a little messed up, but every day it's been improving. So that's what is allowing me to get to phase two [of the concussion protocol], is because everything that I've done, day by day, has been getting better and better. I don't know how long it's going to take, but I'm ahead of the curve as far as the recovery.
"I'm making strong progress a lot faster than they anticipated."
Wright (5-4, 4.09 ERA) has not pitched since Aug. 11 in Miami. The following day, he was hit by a fly ball while running sprints during pregame batting practice.
"It's one of those things, there's not much I can do," Wright said. "After the first two or three days, I was like, 'How could I have avoided it?' I was on my last run. I was done running. How many times are you out in the outfield and you hear, 'Heads up and you don't see the ball? What are the chances of it actually hitting you, let alone hitting you in a spot where it's going to cause so much damage?'"
Wright will be reevaluated on Tuesday after receiving two more days' of treatment at Massachusetts General Hospital. Ultimately, his recovery timetable is entirely dependent on whether he can clear the concussion protocol tests.
"He's progressing through the test," Lovullo said. "He's still having a little balance issue. Major League Baseball does a great job with concussions, and we have to follow the protocol. We can't speed through this."
Alec Shirkey is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.